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Anyone can help figure this out?

Yesterday, while connecting my LED lamp projector with an AC plug, I noticed when one of the 2 pins was connected to the earth pin of my AC extension cord, it would light up slightly. A really weak light but still light.

The extension cord is 20m long but not rolled in a tight coil. It could be somehow like 10 turn of AWG10 wire but I have no idea if that has any impact. The hot wire and neutral are connected but earth is floating.

So now I'm wondering how it's even possible. Could the extension cord induce current and push it into the lamp projector AC-DC transformer enough to light the led slightly? Like the floating earth is acting like an antenna.

I also noticed for a few weeks that my neighbor's lamp is always slightly turned on when turned off. Not sure if it could be related.

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